On attractors of Fibonacci maps

Abstract: In 1990s Bruin, Keller, Nowicki, and van Strien showed that smooth unimodal maps with Fibonacci combinatorics and sufficiently high degree of a critical point have a wild attractor, i.e. their metric and topological attractors do not coincide. However, until now there were no reasonable estimates on the degree of the critical point needed.

In the talk I will present an approach for studying attractors of maps, which are periodic points of a renormalization. Using this approach and rigorous computer estimates, we show that the Fibonacci map of degree d=3.8 does not have a wild attractor, but that for degree d=5.1 the wild attractor exists. The talk is based on a joint work with Denis Gaidashev.

dynamical systemsnumber theory

Audience: researchers in the topic

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One World Numeration seminar

Series comments: Description: Online seminar on numeration systems and related topics

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